Portal:Mathematics
The Mathematics Portal
Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
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- ... that more than 60 scientific papers authored by mathematician Paul Erdős were published posthumously?
- ... that Catechumen, a Christian first-person shooter, was funded only in the aftermath of the Columbine High School massacre?
- ... that A Passage North, which is shortlisted for the 2021 Booker Prize, is set in the aftermath of the Sri Lankan Civil War?
- ... that The Math Myth advocates for American high schools to stop requiring advanced algebra?
- ... that Donn Piatt threw his mathematics teacher out of the window?
- ... that Arithmetic was the first mathematics text book written in the Russian language?
- ... that the number of cannonballs in a square pyramid with cannonballs along each edge is ?
- ... that although the problem of squaring the circle with compass and straightedge goes back to Greek mathematics, it was not proven impossible until 1882?
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- ...that in senary, all prime numbers other than 2 and 3 end in 1 or a 5?
- ...that, for all prime numbers p, the pth Perrin number is divisible by p?
- ...that it is impossible to trisect a general angle using only a ruler and a compass?
- ...that in a group of 23 people, there is a more than 50% chance that two people share a birthday?
- ...that the 1966 publication disproving Euler's sum of powers conjecture, proposed nearly 200 years earlier, consisted of only two sentences?
- ...the hyperbolic trigonometric functions of the natural logarithm can be represented by rational algebraic fractions?
- ... that economists blame market failures on non-convexity?
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Georg Ferdinand Ludwig Philipp Cantor (December 3, 1845, St. Petersburg, Russia – January 6, 1918, Halle, Germany) was a German mathematician who is best known as the creator of set theory. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's theorem implies the existence of an "infinity of infinities." He defined the cardinal and ordinal numbers, and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.
Cantor's work encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré, and later from Hermann Weyl and L.E.J. Brouwer. Ludwig Wittgenstein raised philosophical objections. Nowadays, the vast majority of mathematicians who are neither constructivists nor finitists accept Cantor's work on transfinite sets and arithmetic, recognizing it as a major paradigm shift. (Full article...)
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